A convenience store sold bacon, salmon and club sandwiches. The ratio of the number of bacon sandwiches made to the total number of sandwiches made was 5 : 9. The ratio of the number of salmon sandwiches made to the total number of sandwiches made was 1 : 5. After the store sold some bacon sandwiches and made another 19 salmon sandwiches, there was an equal number of bacon, salmon and club sandwiches left. Find the number of bacon sandwiches sold.

	Bacon	Salmon	Club	Total
Comparing bacon to total	5x5			9x5
Comparing  salmon to total		1x9		5x9
	25 u	9 u	11 u	45 u

	Bacon	Salmon	Club	Total
Before	25 u	9 u	11 u	45 u
Change	- 14 u	+ 19	No change
After	1x11 = 11 u	1x11 = 11 u	1x11 = 11 u

The total number of sandwiches is the same at first. Make the total number of sandwiches the same.  LCM of 5 and 9 is 45.

Number of club sandwiches remains the same at first and in the end. Make the number of club sandwiches the  same. LCM of 1 and 11 is 11.

Number of club sandwiches 
= 45 u - 25 u - 9 u
= 11 u

Number of bacon, salmon and club sandwiches is the same in the end. 

Number of salmon sandwiches = 9 u + 19

9 u + 19 = 11 u
11 u - 9 u = 19
2 u = 19

1 u = 19 ÷ 2 = 9

Number of bacon sandwiches sold
= 25 u - 11 u
= 14 u
= 14 x 9
= 126

Answer(s): 126